Detection Of Known Signals Research Articles

An Exact Solution for Sparse Sampling for Optimal Detection of Known Signals in Gaussian Noise

Detection of known signals of interest that are embedded in colored noise involves whitening the received samples and matched-filtering. In many applications, due to computational constraints, it is critical to select only a subset of the received samples for detection. This paper addresses the problem of selecting only a given number of temporal or spatial samples while maximizing detection performance for deterministic signals in first-order autoregressive Gaussian noise. The direct solution of this entails a combinatorial search, where the deflection coefficient is evaluated for each possible combination of sparse samples. This approach is infeasible when the number of samples is large since the number of possible combinations increases factorially with the number of samples. We present an efficient method to whiten Gaussian noise samples and express deflection coefficient in a form that is amenable to dynamic programming. Exploiting dynamic programming, we specify a feasible and efficient procedure to find optimal sparse samples where the number of computational steps increases linearly with the number of samples. Also, conditions under which uniform sampling is optimal is given.

Rank Correlation Based Detection of Known Signals in Middleton's Class-A Noise

This letter proposes to apply two rank correlations, namely, Kendall's tau (KT) and Spearman's rho (SR), to the fundamental problem of detecting known signals in impulsive noise. Under the popular Middleton's Class-A impulsive noise model, we derived the expectations and variances of KT and SR, which, along with the central limit theorem, are further employed to determing the detection threshold and the detection probability. Monte Carlo simulations not only verified the correctness of our theoretical findings, but also demonstrated the superiority of KT and SR to other five state-of-the-art methods in terms of detection probability.

Detection of known signals in additive impulsive noise based on Spearman’s rho and Kendall’s tau

In this paper, we apply Spearman’s rho (SR) and Kendall’s tau (KT) to the long-lasting problem of detecting known signals in additive impulsive noise. Under a specified contaminated Gaussian model (CGM), which emulates a frequently encountered scenario in radar, sonar and/or communication, we derive the analytic forms of their expectations and variances. For a better understanding of their properties, we further compare SR and KT with three classical detectors, namely, the locally optimal detector (LOD), the matched filter based detector (MFD), and the sign correlator (SC), in terms of the receiver operating characteristic (ROC) curve, area under the ROC curve (AUC), as well as the detection probability. Monte Carlo simulations not only validate our theoretical discoveries, but also demonstrate the advantages of SR and KT in the aspects of 1) accurate false alarm probability control without knowledge of noise distribution, 2) relatively high performances for white Gaussian noise, and 3) gap-bridging properties between LOD and SC in both normal and impulsive noise. The theoretical findings in this work enable SR and KT to be useful alternatives to the MFD and SC whether or not the distribution of noise is Gaussian or Contaminated Gaussian.

A Novel Approach to Signal Detection of Sensor Array Units Using 5-3-1 Rule Based Matched Filter Algorithm with Intelligent Identifiers

A novel approach to signal detection and identific ation was developed and tested. The new algorithm was based on provision of tagging a Matched Filter (MF) with identifiers to recognize the source signal with and without noise, so that class ification can be carried out. The algorithm was applied successfully to chemical Sensor Array Units (SAU). Problem statement: Signals obtained from chemical sensors were sometimes contaminated with noise. Detection of known signals from noisy surroundings was critical in the field of sen sors and their applications. Approach: Six chemical sensor array units were tested at different gas con centrations. The testing was carried out under norm al conditions and with the presence of noise. The deve loped algorithm was then applied to detect, identif y and classify the results. Results: The 5-3-1 algorithm produced symmetrical arrays with the source signal identifiers at the corners. The symmetry all owed the use of one-third of the produced data for identification, saving processing time and memory s torage. Conclusion: The obtained data also proved that gap separation between conducting electrodes t o inversely affect device conductance, with different gap widths affected similarly with temper ature change per constant deposited film thickness. Also, each device conductance increased in response to increase in applied gas concentration.

What limits performance in the amblyopic visual system: Seeing signals in noise with an amblyopic brain

Amblyopia results in a loss of visual acuity, contrast sensitivity, and position acuity. However, the nature of the neural losses is not yet fully understood. Here we report the results of experiments using noise to try to better understand the losses in amblyopia. Specifically, in one experiment we compared the performance of normal, amblyopic, and ideal observers for detecting a localized signal (a discrete frequency pattern or DFP) in fixed contrast white noise. In a second experiment, we used visibility-scaled noise and varied both the visibility of the noise (from 2 to 20 times the noise detection threshold) and the spatial frequency of the signal. Our results show a loss of efficiency for detection of known signals in noise that increases with the spatial frequency of the signal in observers with amblyopia. To determine whether the loss of efficiency was a consequence of a mismatched template, we derived classification images. We found that although the amblyopic observers' template was shifted to lower spatial frequencies, the shift was insufficient to account for their threshold elevation. Reduced efficiency in the amblyopic visual system may reflect a high level of internal noise, a poorly matched position template, or both. To analyze the type of internal noise we used an "N-pass" technique, in which observers performed the identical experiment N times (where N = 3 or 4). The amount of disagreement between the repeated trials enables us to parse the internal noise into random noise and consistent noise beyond that due to the poorly matched template. Our results show that the amblyopes' reduced efficiency for detecting signals in noise is explained in part by reduced template efficiency but to a greater extent by increased random internal noise. This loss is more or less independent of external noise contrast over a log unit range of external noise.

Detection of known signals in 1/f fractal noise

Based on the whitening property of wavelet transformation for 1/f noise, this paper addresses the problem of detecting deterministic signals in the presence of 1/f fractal noise. The transfer function of whitening filter is provided as well as the condition for whitening. The receiver structure based on Karhunen-Loeve expansion and the decision rule are also given. Finally performance of the detector is analyzed.

Nonparametric detection of known signals based on ranks in multiplicative noise

Multiplicative noise is known to be useful in modeling multipath propagation which is important in mobile communication systems. In this paper, nonparametric detection of known signals in multiplicative noise is considered. The locally optimum detector is derived based on signs and ranks of observations for good weak-signal detection performance under any specified noise probability density function. This detector has similarities to the locally optimum detector for known signals in multiplicative noise. The asymptotic performance of this nonparametric detector is as good as that of the locally optimum detector. With approximate score functions, we can construct the approximate locally optimum rank detector.

Nonparametric detection of known signals based on ranks in multiplicative noise

Abstract Multiplicative noise is known to be useful in modeling multipath propagation which is important in mobile communication systems. In this paper, nonparametric detection of known signals in multiplicative noise is considered. The locally optimum detector is derived based on signs and ranks of observations for good weak-signal detection performance under any specified noise probability density function. This detector has similarities to the locally optimum detector for known signals in multiplicative noise. The asymptotic performance of this nonparametric detector is as good as that of the locally optimum detector. With approximate score functions, we can construct the approximate locally optimum rank detector.

Adaptive detection of known signals in additive noise by means of kernel density estimators

We consider the problem of detecting known signals contaminated by additive noise with a completely unknown probability density function f. To this end, we propose a new adaptive detection rule. It is defined by plugging a kernel density estimator f/spl circ/ of f into the maximum a posteriori (MAP) detector. The estimate f/spl circ/ can either be computed off-line from a training sequence or on-line simultaneously with the detection. For the off-line detector, we prove that the (asymptotic) error probability for weak signals converges to the minimal error probability of the MAP detector as the number of training data tends to infinity, and we also establish rates of convergence and the optimal choice of bandwidth order for a certain class of noise densities. In a Monte Carlo study, the off-line plug-in MAP detectors are compared with the L/sup 1/- and L/sup 2/-detectors for various noise distributions. When the training sequence is long enough, the plug-in detectors have excellent performance for a wide range of distributions, whereas the L/sup 2/-detector breaks down for heavy-tailed distributions and the L/sup 1/-detector for distributions with little mass around the origin.

A known-signal detector based on ranks in weakly dependent noise

Locally optimum rank detection of known signals under a weakly dependent noise model is considered in this paper. The weakly dependent noise model is known to be useful for modeling inter-user interference, which is important in the synthesis and analysis of mobile communication systems. For good weak-signal detection performance under any specified noise probability density function, the locally optimum detector is derived based on signs and ranks of the observation. It is also shown that the locally optimum rank detector has the same asymptotic performance as the locally optimum rank detector which uses the actual values of the observations.

Performance characteristics of the fuzzy sign detector

In this paper, fuzzy statistical techniques are introduced into the optimum signal detection problems. The likelihood ratio for fuzzy detection of known signals is obtained. As a special case of the fuzzy signal detector, a fuzzy set theoretic approach to sign detection of known signals is considered. Specifically, the test statistic of the fuzzy sign detector for known signals is obtained. Some properties of the fuzzy sign nonlinearity, which constitutes the fuzzy sign detector, are also described. Finally, the performance characteristics of the fuzzy sign detector are investigated and compared to those of the crisp sign detector.

Asymptotically robust detection of known signals in nonadditive noise

Robust detection of known weak signals of unknown amplitude is considered for a class of combined additive and nonadditive noise models and an asymptotically large set of independent observations. This class includes observation models that may have combinations of multiplicative and signal-dependent noise terms. Sufficient conditions are given for robust detection schemes for cases where the general form of the observation model is known but the additive noise distribution is known only to be a member of a general convex uncertainty class. Robust schemes satisfying these conditions are found for some example cases where additive signals and noise have been processed by memoryless nonlinearities. Some interesting example cases of combined multiplicative and signal-dependent noise are shown to use redescending nonlinearities, instead of the limiter nonlinearities typically found for similar additive noise cases. >

A fuzzy set theoretic approach to weak known-signal detection

Abstract In this paper locally optimum detection of known signals is considered when the observations provide us with fuzzy information, and a useful expression of the test statistic of the locally optimum fuzzy detector for known signals is obtained. The structure of the locally optimum fuzzy detector is obtained and compared to that of the classical (crisp) locally optimum detector. Several properties of the locally optimum fuzzy nonlinearity, which constitutes the locally optimum fuzzy detector, are also described.

Robust detection of known signals in asymmetric noise

The detection of signals in noise with possibly asymmetric probability density functions is considered. The noise density model allows a symmetric contaminated-nominal central part and an arbitrary tail behavior. For detection of known signals, the robust nonlinear-correlator (NC) detector is obtained based on detector efficacy as performance criterion. The robust <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</tex> -detector structure for constant-signal detection is also explicitly obtained.

On single-sample robust detection of known signals with additive unknown-mean amplitude-bounded random interference--II: The randomized decision rule solution (Corresp.)

A randomized decision rule is derived and proved to be the saddlepoint solution of the robust detection problem for known signals in independent unknown-mean amplitude-bounded noise. The saddlepoint solution \phi^{0} uses an equaUy likely mixed strategy to chose one of N Bayesian single-threshold decision rules \phi_{i}^{0}, i = 1,\cdots , N having been obtained previously by the author. These decision rules are also all optimal against the maximin (least-favorable) nonrandomized noise probability density f_{0} , where f_{0} is a picket fence function with N pickets on its domain. Thee pair (\phi^{0}, f_{0}) is shown to satisfy the saddlepoint condition for probability of error, i.e., P_{e}(\phi^{0} , f) \leq P_{e}(\phi^{0} , f_{0}) \leq P_{e}(\phi, f_{0}) holds for all f and \phi . The decision rule \phi^{0} is also shown to be an eqoaliir rule, i.e., P_{e}(\phi^{0}, f ) = P_{e}(\phi^{0},f_{0}) , for all f , with 4^{-1} \leq P_{e}(\phi^{0},f_{0})=2^{-1}(1-N^{-1})\leq2^{-1} , N \geq 2 . Thus nature can force the communicator to use an {\em optimal} randomized decision rule that generates a large probability of error and does not improve when less pernicious conditions prevail.

On single-sample robust detection of known signals with additive unknown-mean amplitude-bounded random interference

The single-sample robust decision problem for known signals in additive unknown-mean amplitude-bounded random interference is investigated. The approach is based on the generalized Lagrange multiplier theory for infinite-dimensional linear spaces. For the probability-of-error performance measure (Bayes risk) and equally likely binary signaling both minimax and maximin subproblems are formulated and solved explicitly. There is no nonrandomized saddlepoint solution. Moreover, the respective solutions are not unique and the classes of maximin and minimax decision rules are not disjoint. A uniform density and its optimal decision rule are shown to yield performance slightly less than the maximin value.

Nearly optimal detection of known signals in correlated Gaussian noise

The problem of detecting a known signal in correlated Gaussian noise is considered. The Neyman-Pearson optimal detector for this problem is, of course, well known. Unfortunately, unless the number of observations is small, the amount of computation required to design this optimal detector can be quite substantial. For this reason, two suboptimal detectors are introduced which, for a given noise autocorrelation matrix, are much easier to design than the optimal detector. Both suboptimal detectors are based on simple modifications of the white-noise detector, and yet their performance, in many instances, is nearly optimal. In addition, a numerical study is presented which indicates that these detectors are much less sensitive to changes in the underlying noise autocorrelation function than is the Neyman-Pearson optimal detector.

Robust detection of known signals

The problem of detection of known signals in additive noise is solved under the assumption that the unknown noise density is a member of some known family of symmetric densities. A general approach to the design of receivers that are asymptotically most robust is established. As an example, a detector is derived by applying the procedure to the special case obtained when the noise density family is defined by F=\left\{f \left| \int^{a}_{-a} f(x) dx = p, f \mbox{symmetric} \right}. Simulation results showing the detector's performance for small sample sizes are provided.

Optimum detection and signal design for v.l.f. channels

A new generalized model for atmospheric radio noise is briefly described and justified by comparison with observed probability distributions. A special case of this generalized model is then compared to the observed noise statistics at the very low frequency end of the spectrum. This model is then applied to the detection of known signals in in the presence of noise to determine the optimal receiver structure. The performance of the detector, specified by the upper bound on the probability of error, is assessed and is seen to depend on the signal shape, the time-bandwidth product, and signal-to-noise ratio. The optimal signal to minimize the probability of error is then determined.

Signal Detection in the Presence of Atmospheric Noise in Tropics

A new model of HF atmospheric radio noise (ARN) that leads to observed probability distributions of noise is briefly described. The new ARN model is then applied to the detection of known signals in the presence of noise to determine optimal receiver structure for ARN. Probabilities of errors for a linear matched filter and nonlinear (-1/log) and inverted (log)^{2} correlator receivers and a phase coherent binary detector are determined and compared. It is shown that the inverted (log)^{2} correlator combined with the linear matched filter is an optimal receiver in the presence of impulsive noise in tropics. The time statistics of burst noise is applied to design of signals for improved reliability.